Question

x is the length in inches of the third side of a triangle. the range of all possible values of x is shown on the number line. which of the following options has possible lengths of the other two sides of the triangle? (1 point) 42 inches and 50 inches 28 inches and 64 inches 36 inches and 92 inches 48 inches and 76 inches

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third - side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies \(|a - b|\lt x\lt a + b\).

Step2: Check each option

Option 1: \(a = 42\), \(b = 50\)

\(a + b=42 + 50=92\), \(|a - b|=|42 - 50| = 8\). The range of \(x\) is \(8\lt x\lt92\), not \(36\lt x\lt92\).

Option 2: \(a = 28\), \(b = 64\)

\(a + b=28+64 = 92\), \(|a - b|=|28 - 64|=36\). The range of \(x\) is \(36\lt x\lt92\).

Option 3: \(a = 36\), \(b = 92\)

\(a + b=36 + 92=128\), \(|a - b|=|36 - 92| = 56\). The range of \(x\) is \(56\lt x\lt128\), not \(36\lt x\lt92\).

Option 4: \(a = 48\), \(b = 76\)

\(a + b=48 + 76=124\), \(|a - b|=|48 - 76| = 28\). The range of \(x\) is \(28\lt x\lt124\), not \(36\lt x\lt92\).

Answer:

28 inches and 64 inches